In general, no, it is not readily accessible. Data is generally kept in unspecified locations in memory, formatted for ease of computation.

Sometimes hackers piece together where bits of data are stored in order to manipulate it. This obviously is not supported, and may not even be legal.

There are simulators that go out of their way to expose that kind of information. For example, X-Plane allows developers to write plugins, and it sends all sorts of information to those plugins including velocity and acceleration (at least, that what I believe to be true based on what I read here: http://wiki.openpilot.org/display/Doc/HiTL+Plugin). But most games don't bother with this.

If there are specific games you are interested in, check to see if they are open source, have a plugin architecture, a public SDK, or are designed to be modifiable by end users ("moddable", "mod-friendly"). But even in those cases there is no guarantee that the information you want will be easy to get. A better indicator is if there is a community of enthusiasts that build devices to work with a particular game. Flight simulators are the classic example, maybe there are others.

It's possible that widely-used engines like the Quake engine make the information readily accessible, as part of their debugging tools. But I suspect the public information has more to do with the level design and monster attributes and scripted events than the game's physics. (Maybe someone with hands-on experience will comment.)

Short answer is, I believe it's going to be a pain for most games, and each game is going to be different.